“We expected a charm offensive. We readied ourselves for a possible diplomatic breakthrough. But we were left underwhelmed,” they wrote.

“In the coming days, we will be outspoken in our support for furthering sanctions against Iran, requiring countries to again reduce their purchases of Iranian petroleum and imposing further prohibitions on strategic sectors of the Iranian economy.”

The senators outlined “four strategic elements” they say are “necessary to achieve a resolution of this issue: an explicit and continuing message that the United States will not allow Iran to acquire a nuclear weapons capability, a sincere demonstration of openness to negotiations by Iran, the maintenance and toughening of sanctions and a convincing threat of the use of force.”

They said they had been “cautiously hopeful” ahead of Rouhani's visit to the U.N. General Assembly in New York last week. But they said they were disappointed by several incidents, including Rouhani's criticism of the United States and Israel in his U.N. speech and his “weak” decision not to meet with Obama for a handshake, although the two spoke by phone on Friday – the first direct conversation between presidents of the two countries since the 1979 Islamic revolution.